Optimal. Leaf size=20 \[ \frac{1}{2} e^{2 x} x-\frac{e^{2 x}}{4} \]
[Out]
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Rubi [A] time = 0.0144578, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.286 \[ \frac{1}{2} e^{2 x} x-\frac{e^{2 x}}{4} \]
Antiderivative was successfully verified.
[In] Int[E^(2*x)*x,x]
[Out]
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Rubi in Sympy [A] time = 1.13688, size = 14, normalized size = 0.7 \[ \frac{x e^{2 x}}{2} - \frac{e^{2 x}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(exp(2*x)*x,x)
[Out]
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Mathematica [A] time = 0.00214549, size = 15, normalized size = 0.75 \[ e^{2 x} \left (\frac{x}{2}-\frac{1}{4}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[E^(2*x)*x,x]
[Out]
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Maple [A] time = 0.003, size = 12, normalized size = 0.6 \[{\frac{ \left ( 2\,x-1 \right ){{\rm e}^{2\,x}}}{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(exp(2*x)*x,x)
[Out]
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Maxima [A] time = 1.35264, size = 15, normalized size = 0.75 \[ \frac{1}{4} \,{\left (2 \, x - 1\right )} e^{\left (2 \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*e^(2*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.2061, size = 15, normalized size = 0.75 \[ \frac{1}{4} \,{\left (2 \, x - 1\right )} e^{\left (2 \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*e^(2*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.064042, size = 10, normalized size = 0.5 \[ \frac{\left (2 x - 1\right ) e^{2 x}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(exp(2*x)*x,x)
[Out]
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GIAC/XCAS [A] time = 0.20213, size = 15, normalized size = 0.75 \[ \frac{1}{4} \,{\left (2 \, x - 1\right )} e^{\left (2 \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*e^(2*x),x, algorithm="giac")
[Out]